Jobocan might be able to give more specifics, but I can give you some resources for the worst case scenario that it is something else.
After much drama, ebay bidding, and such. SMSPower obtained and uploaded the service manuals for the master system and game gear. Here is the HTML version of the master system manual (just 3 weeks old)
http://www.smspower.org/Development/SegaMasterSystemServiceManualDo you have a Genesis model 1? The simplest thing will be to try that AC adapter and AV cable. A lot of times, that fixes what you describe. Also, I have purchased several "as parts" items from ebay and just after a good cleaning inside, they work perfectly. Some people seem to bury their game systems in dirt and cigarettes before playing them. One time I found a buck in change in a Genesis!
I would do the above first no matter what. Always clean them out. Then troubleshoot using the service manual.